## Cipher

A cipher is defined over the spaces of: All Keys, \(\mathscr{K}\) All Messages, \(\mathscr{M}\) All Cipher texts, \(\mathscr{C}\) Cipher (defined as a triple, \((\mathscr{K}, \mathscr{M}, \mathscr{C})\)) as a pair of algorithms \((\mathbf{E}, \mathbf{D})\) where \(\mathbf{E}\) represents the encryption algorithm and \(\mathbf{D}\) represents the decryption algorithm. \begin{equation} \mathbf{E}: \mathscr{K} \times \mathscr{M} \rightarrow \mathscr{C} \end{equation} and \begin{equation} \mathbf{D}: \mathscr{K} \times \mathscr{C} \rightarrow \mathscr{M} \end{equation} Such that: \begin{equation} \forall m \in \mathscr{M}, k \in \mathscr{K}: \mathbf{D}(k, \mathbf{E}(k, m)) = m \end{equation} ...